Commutation of Annual Subscriptions

Commutation Structures

For fixed object X in a monoidal category, an X-commutation structure on an object A is just a map X⊗A → A⊗X. We study aspects of such structures in case A has a dual object. We consider a monoidal category V,⊗, I; for simplicity we let it be strict (the application we have in mind is anyway a category of endofuncors on a category, with composition as ⊗). Let X be an object in V, fixed througho...

Challenges of Commutation

We consider a few problems connected to the commutation of languages, in particular nite ones. The goal is to emphasize the challenging nature of such simply formulated problems. In doing so we give a survey of results achieved during the last few years, restate several open problems and illustrate some approaches to attack such problems by two simple constructions.

Partial Commutation and Traces

Commutation of Cellular Automata Rules

This paper addresses the following problem: Given a onedimensional cellular automata (CAl defined over Z2 with a rule represented by an operat or X , determine all one-dimensional rules over Z2 which commute with X . It is shown th at the set of all such rules is given by th e solut ion set of a system of nonlinear Diophantine equations. This result is generalized to cover cellular automata who...

Commutation with codes

The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...